Draper, 24, has ensured a disrupted season after injuring his arm at the US Open in August last year.
He was due to face sixth seed Taylor Fritz in the first round on Centre Court on Tuesday.
"Devastated to share that I have had to withdraw from my first round match due to a recurrence of my arm injury," Draper said.
"There have been a lot of painful moments in the last 12 months, but this one is definitely the absolute worst, as there is no greater honour for a British player than playing at Wimbledon.
"I will continue to persevere through this. Thank you for the support."
It is a huge blow for Draper, who appointed Andy Murray as his coach for the grass-court season.
Draper had a positive warm-up to Wimbledon as he reached the semi-finals of the Eastbourne Open.
Draper follows Emma Raducanu in withdrawing before the tournament through injury.
Raducanu – the former US Open champion – pulled out ahead of the first round due to a stress fracture in her leg.